Current Algebras and Groups

  • Jouko Mickelsson

Part of the Plenum Monographs in Nonlinear Physics book series (PMNP)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Jouko Mickelsson
    Pages 1-20
  3. Jouko Mickelsson
    Pages 21-42
  4. Jouko Mickelsson
    Pages 43-74
  5. Jouko Mickelsson
    Pages 75-104
  6. Jouko Mickelsson
    Pages 105-126
  7. Jouko Mickelsson
    Pages 127-170
  8. Jouko Mickelsson
    Pages 171-191
  9. Jouko Mickelsson
    Pages 193-202
  10. Jouko Mickelsson
    Pages 203-233
  11. Jouko Mickelsson
    Pages 235-244
  12. Jouko Mickelsson
    Pages 245-265
  13. Back Matter
    Pages 299-313

About this book


Let M be a smooth manifold and G a Lie group. In this book we shall study infinite-dimensional Lie algebras associated both to the group Map(M, G) of smooth mappings from M to G and to the group of dif­ feomorphisms of M. In the former case the Lie algebra of the group is the algebra Mg of smooth mappings from M to the Lie algebra gof G. In the latter case the Lie algebra is the algebra Vect M of smooth vector fields on M. However, it turns out that in many applications to field theory and statistical physics one must deal with certain extensions of the above mentioned Lie algebras. In the simplest case M is the unit circle SI, G is a simple finite­ dimensional Lie group and the central extension of Map( SI, g) is an affine Kac-Moody algebra. The highest weight theory of finite­ dimensional Lie algebras can be extended to the case of an affine Lie algebra. The important point is that Map(Sl, g) can be split to positive and negative Fourier modes and the finite-dimensional piece g corre­ sponding to the zero mode.


algebra model operator statistical physics transformation

Authors and affiliations

  • Jouko Mickelsson
    • 1
  1. 1.University of JyväskyläJyväskyläFinland

Bibliographic information

  • DOI
  • Copyright Information Springer Science+Business Media New York 1989
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4757-0297-2
  • Online ISBN 978-1-4757-0295-8
  • Buy this book on publisher's site